We show the special dynamic characteristic of Gaussian quantum discord, exhibited by two-mode Gaussian symmetric squeezed thermal states (STS) in continuous-variable (CV) systems with a common non-Markovian environment, is definitely different from Markov processes. We demonstrate that Gaussian quantum discord can be created whenever the information flow from environment back to the system. We also show that the rate of decrease for Gaussian quantum discord is related to the coupling constant. We discover that the initial value of Gaussian quantum discord is determined by the average number of thermal photons of the system.